Angular Impulse-Momentum Principle - Example Problem 9.7-5

 

Four masses (m) are attached to a light shaft. The masses are located a distance r from the axis of rotation. The shaft rotates through the action of a belt system suspended on frictionless bearings. The force T is applied to a belt wrapped around a pulley of radius r_p. You may assume the belt is inextensible and doesn't slip on the pulley. If the system starts from rest, determine the time it will take for the system to reach an angular velocity of ω.

 

 

Given:

• ω_o = 0

 

Find:

• Δt

 

Determine the time it takes for the system to reach an angular speed of ω

 

Δt = 4r²mω/(Tr_P )
Δt = 4rmω/T
Δt = 4mω/(Tr_P )